Problem: On the first 6 exams of her language class, Emily got an average score of 79. What does she need on the next exam to have an overall average of 82?
Let her score on the next exam be $x$ The sum of all of her scores is then $6 \cdot 79 + x$ The same sum must also be equal to $7 \cdot 82$ Solve: $x = 7 \cdot 82 - 6 \cdot 79 = 100$.